The problem asks us to calculate how many articles a factory produces in a day, given the following information:

• There are 18 machines.
• Each machine works 10 hours per day.
• Each machine produces 165 articles per hour.

To find the total number of articles produced in a day, we can use the following steps:

1. Find the number of articles produced by one machine in a day:

   • Articles produced per hour by one machine = 165
   • Hours worked per day = 10
   • Articles produced by one machine in a day = 165 * 10 = 1650

2. Find the total number of articles produced by all 18 machines:

   • Total articles produced by 18 machines = 1650 * 18 = 29,700

Thus, the factory produces 29,700 articles in a day.

Let me know if you'd like further details or have any questions about the calculation.

Here are some related questions for further exploration:

1. What if the machines worked for 12 hours instead of 10 hours? How many articles would the factory produce?
2. How would the production change if the factory had 20 machines instead of 18?
3. If each machine produced 200 articles per hour, how many articles would the factory produce in a day?
4. How do you calculate the total output for a factory with different types of machines working different hours?
5. What are the effects on production when there are maintenance downtimes?

Tip: Always break down word problems into smaller parts and solve step by step!